Other Applied Mathematics Commons^™

Bringing Gans To Medieval Times: Manuscript Translation Models, Tonilynn M. Holtz

College of Graduate Studies: Theses & Dissertations

The Generative Adversarial Networks (GAN) recently emerged as a powerful framework for producing new knowledge from existing knowledge. These models aim to learn patterns from input data then use that knowledge to generate output data samples that plausibly appear to belong to the same set as the input data. Medieval manuscripts study has been an important research area in the humanities field for many decades. These rare manuscripts are often times inaccessible to the general public, including students in scholars, and it is of a great interest to provide digital support (including, but not limited to translation and search) for …

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

College of Graduate Studies: Theses & Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan

College of Graduate Studies: Theses & Dissertations

The understanding of Bender Element mechanism and utilization of Particle Flow Code (PFC) to simulate the seismic wave behavior is important to test the dynamic behavior of soil particles. Both discrete and finite element methods can be used to simulate wave behavior. However, Discrete Element Method (DEM) is mostly suitable, as the micro scaled soil particle cannot be fully considered as continuous specimen like a piece of rod or aluminum. Recently DEM has been widely used to study mechanical properties of soils at particle level considering the particles as balls. This study represents a comparative analysis of Voigt and Best …

Eeg Signals Classification Using Lstm-Based Models And Majority Logic, James A. Orgeron

College of Graduate Studies: Theses & Dissertations

The study of elecroencephalograms (EEGs) has gained enormous interest in the last decade with the increase of computational power and availability of EEG signals collected from various human activities or produced during medical tests. The applicability of analyzing EEG signals ranges from helping impaired people communicate or move (using appropriate medical equipment) to understanding people's feelings and detecting diseases.

We proposed new methodology and models for analyzing and classifying EEG signals collected from individuals observing visual stimuli. Our models rely on powerful Long-Short Term Memory (LSTM) Neural Network models, which are currently the state of the art models for performing …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

College of Graduate Studies: Theses & Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

Modeling The Stock Market Through Game Theory, Kylie Hannafey

Honors College Theses

Game Theory is used on many occasions to help us understand interactions between decision-makers. The famous Nash equilibrium is a steady state in a model that shows the interaction of different players, in which no player can do better by choosing a different action if the actions of the other players do not change. These two concepts can be applied to numerous situations that vary in types of players, but for our research, we are focusing on businesses in the stock market. The main objective is to use Game Theory to analyze data collected from the stock market, model our …

Arnold Transformations As Applied To Data Encryption, Haley N. Anderson

College of Graduate Studies: Theses & Dissertations

As our world becomes increasingly digital, data security becomes key. Data must be encrypted such that it can be easily encrypted only by the intended recipient. Arnold Transformations are a useful tool in this because of its unpredictable periodicity. Our goal is to outline a method for choosing an Arnold Transformation that is both secure and easy to implement. We find the necessary and sufficient condition that a key matrix has periodicity. The chosen key matrix has a random structure, and it has a periodicity that is sufficiently high. We apply this method to several image and data string examples …

Implementing A Neural Network For Supervised Learning With A Random Configuration Of Layers And Nodes, Kane A. Phillips

College of Graduate Studies: Theses & Dissertations

Deep learning has a substantial amount of real-life applications, making it an increasingly popular subset of artificial intelligence over the last decade. These applications come to fruition due to the tireless research and implementation of neural networks. This paper goes into detail on the implementation of supervised learning neural networks utilizing MATLAB, with the purpose being to generate a neural network based on specifications given by a user. Such specifications involve how many layers are in the network, and how many nodes are in each layer. The neural network is then trained based on known sample values of a function …

Association Rules Patterns Discovery From Mixed Data, Welendawa Acharige Charith A. Elson

College of Graduate Studies: Theses & Dissertations

Finding Association Rules has been a popular unsupervised learning technique for dis covering interesting patterns in commercial data for well over two decades. The method seeks groups of data attributes and their values where their probability density of these attributesattherespectivevaluesismaximized. Therearecurrentlywell-establishedmeth ods for tackling this problem for data with categorical (discrete) attributes. However, for the cases of data with continuous variables, the techniques are largely focusing on cate gorizing continuous variables into intervals of interest and then relying on the categorical data methods to address the problem. We address the problem of finding association rules patterns in mixed data by …

Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam

College of Graduate Studies: Theses & Dissertations

The automatic character recognition task has been of practical interest for a long time. Nowadays, there are well-established technologies and software to perform character recognition accurately from scanned documents. Although handwritten character recognition from the manuscript image is challenging, the advancement of modern machine learning techniques makes it astonishingly manageable. The problem of accurately recognizing handwritten character remains of high practical interest since a large number of manuscripts are currently not digitized, and hence inaccessible to the public. We create our repository of the datasets by cropping each letter image manually from the manuscript images. The availability of datasets is …

Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins

College of Graduate Studies: Theses & Dissertations

In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …

Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

College of Graduate Studies: Theses & Dissertations

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …

Multiclass Classification Using Support Vector Machines, Duleep Prasanna W. Rathgamage Don

College of Graduate Studies: Theses & Dissertations

In this thesis, we discuss different SVM methods for multiclass classification and introduce the Divide and Conquer Support Vector Machine (DCSVM) algorithm which relies on data sparsity in high dimensional space and performs a smart partitioning of the whole training data set into disjoint subsets that are easily separable. A single prediction performed between two partitions eliminates one or more classes in a single partition, leaving only a reduced number of candidate classes for subsequent steps. The algorithm continues recursively, reducing the number of classes at each step until a final binary decision is made between the last two classes …

Applications Of Flow Network Models In Finance, Angel J. Woods

College of Graduate Studies: Theses & Dissertations

In this thesis we explore the applications of flow networks in practical problems in finance. After introducing basic definitions and background information, we first survey some known applications of flow networks in theoretical mathematics. We also briefly comment on their potential applications in the setting of financial flow networks. We then construct networks from practical financial flows and present the construction, reasoning, and known applications. Lastly, we show a design of financial flow networks that takes time into consideration and discuss its applications.

Drawing Numbers And Listening To Patterns, Loren Zo Haynes

Honors College Theses

The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space …

Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty

Honors College Theses

As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete …

Geometric-Based Algorithm For A Full Row-Rank System Matrix Along Multiple Directions In Dt, Igor Lutsenko

College of Graduate Studies: Theses & Dissertations

Discrete tomography (DT) is an image reconstruction procedure that deals with computational synthesis of a cross-sectional image of an object from either transmission or reflection data collected by penetrating an object with X-rays from a small number of different directions, and whose range of the underlying function is discrete. Image reconstruction using algebraic approach is time consuming and the computation cost depends on the size of the system matrix. More scanning directions provide an increase in the reconstructed image quality, however they increase the size of the system matrix dramatically. Deletion of linearly dependent rows of this matrix is necessary …

Black-Scholes Equation And Heat Equation, Charles D. Joyner

Honors College Theses

First, we present and define the Black-Scholes equation which is used to model assets on the stock market. After that, we derive the heat equation that describes how the temperature increases through a homogeneous material. Finally, we detail how the two equations are related. We introduce and relate the Black-Scholes equation and Heat Equation.

A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach

College of Graduate Studies: Theses & Dissertations

In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model

Solutions Of Inequality Constrained Spline Optimization Problems With The Active Set Method, Joshua A. Holloway

College of Graduate Studies: Theses & Dissertations

We solve the problem of finding a near-interpolant curve, subject to constraints, which minimizes the bending energy of the curve. Using B-splines as our tools, we give a brief overview of spline properties and develop several different cases of inequality constrained optimization problems of this type. In particular, we develop the active set method and use it to solve these problems, emphasizing the fact that this algorithm will converge to a solution in finite iterations. Our solution will solve an open problem regarding near-interpolant spline curves. Furthermore, we supplement this with an iterative technique for better choosing data sites so …

Graphs Of Classroom Networks, Rebecca Holliday

College of Graduate Studies: Theses & Dissertations

In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism …

Enumerating Graphs Using Integrals From Quantum Field Theory, William A. Coggins

College of Graduate Studies: Theses & Dissertations

Enumerating graphs is a relatively new subfield of mathematics. In this thesis, we will discuss a enumerative method that derives from Quantum Field Theory. We begin with the basic ideas of Calculus and extend them into a enumerative method that will allow us to classify graphs embedded on surfaces.

Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith

College of Graduate Studies: Theses & Dissertations

Polynomial surfaces used in ray tracing have recently been improved upon allowing for three dimensional applications. Among these are surfaces that have a varying eccentricity. This paper will discuss a method for finding real roots of polynomials [allowing us to create these surfaces]. First, we will give the reader a basic comprehension of the workings of a ray tracer, a general understanding of three dimensional polynomial surfaces, how this newly implemented root finder functions, and how these concepts enable us to create surfaces of variable eccentricity. Then, examples will be provided to demonstrate the capabilities of the program.

Area Based Fan Beam Projection Model For Computed Tomography, Phillip J. Stevens

Phi Kappa Phi Research Symposium (Archived)

Computed tomography (CT) is image reconstruction of objects using computer processed transmission or reflection data, usually referred to as projection data, from x-ray scanning. This projection data is often modeled using line integrals, but x-rays are of finite width in reality, so the accuracy of the projection data can be improved if an area based approach is used instead. In addition emitter beam shapes affect the reconstruction effectiveness and data collection efficiency, with the two main types of beam choice for 2-D scanning being fan beam and parallel beam. Fan beam scanning offers some advantages over parallel beam, such as …

Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford

College of Graduate Studies: Theses & Dissertations

Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …